JP4362766B2 - Gravity deviation meter - Google Patents

Description

Field of use

CROSS REFERENCE TO RELATED PATENT This application claims priority from US Provisional Application No. 60 / 361,699, filed March 6, 2002, the contents of which are incorporated herein by reference. It is.

  Geologists have discovered that certain physical properties related to geology can be revealed from the field of gravity potential near the geology (denoted here by the symbol G). For example, the gravity field G can reveal and identify the presence of minerals such as coal below the surface of the geology. Therefore, by measuring and analyzing the gravity field G, it is possible to know the physical characteristics of the geology more easily and less costly than intrusion methods such as excavation. Field-related properties generally do not directly measure the gravitational potential G, but instead measure the components of the gravitational acceleration vector g based on this field, or measure the spatial derivatives of these acceleration vector components Decide by. Spatial differentiation of the three components of the acceleration vector with respect to three different axes yields nine different combinations of signals that are mathematically related to the gravitational potential G of interest. These nine signals are gravity tensor elements (also called gravity gradients), and great efforts have been made so far to develop a method for measuring these tensor elements with high accuracy.

ここで、各行列要素は、重力偏差計10の体心12で交わる三の「本体」の軸 X、Y、およ
びZ の方向の重力テンソルを表す。例えば、テンソル要素Γxxは、重力加速度ベクトルg
のX成分のX軸に対する空間部分導関数である（ここで、テンソル要素は当量単位（メートル/秒^２）/メートルすなわち1/秒^２、またはエトヴェス単位で表され、109エトヴェス＝1/秒^２である）。また、ΓxyはgのX成分のY軸に対する空間部分導関数であり、ΓxzはgのX成分のZ軸に対する空間部分導関数であり、ΓyxはgのY成分のX軸に対する空間部分導関数である。さらに、テンソル要素Γは時間に対して変化し得るものであるが、多くの地質の場合に、テンソル要素Γが時間に対して一定であったり、または時間に対して一定として取り扱ってもよいほどゆっくりと変化する。また、場合によっては、重力偏差計10は、全テンソルΓのうちの所要の要素だけを計算すれば十分であるような測定をする場合もある。次に、地質（図1には示していない）の重力ポテンシャルの場Gを測定するために、重力偏差計10をヘリコプタ等の乗物（図示せず）に搭載し、地形の上空から重力偏差計が走査する場合がある。このように地質を上空から走査している時には、最高の精度を得るためには、重力偏差計10は本体軸X、Y、およびｚを中心にして高速度で回転しないことが望まれる。しかし都合の悪いことには、乗物はしばしば振動を発生したり（例えばエンジンによって）、または振動を受けたりして（例えば風によって）、本体軸が回転を受けてしまう。従って、重力偏差計10は、多くの場合ジンバル装置（図示せず）によって乗物からの回転を遮断し、乗物が作動する際に不可避な方向転換を受けた場合においてすら、重力偏差計は非回転を維持するようになっている。重力偏差計10を搬持しているジンバル装置は、一般的にジャイロスコープ組立体等の回転センサ組立体18を備えており、本体軸X、Y、およびZを中心とする回転運動（一般的には回転速度ωまたは回転変位）を測定するようになっている。これらの測定値から得られる制御信号が、ジンバル装置軸に付随しているモータにフィードバックされ、重力偏差計10の受けている回転を低減させる。しかしながら、振動によって誘導された重力偏差計10の回転の程度を、ジンバル装置によって一般的に低減するとは言っても、これらの回転を全て消滅させることは不可能である。従って、テンソル測定は、仮に理想的な偏差計を使用したとしても、上記のような回転に起因する勾配信号の存在によって阻害される可能性があることは物理的に避けることができない。これらの付加的な重力によるものではない勾配（偏差）は、回転速度から簡単に決定することができる関数である（例えば本体軸jを中心とする回転速度をωjラジアン/秒としたときに、回転によるΓ＝ωx,ωyである）。従って、偏差計10からの測定値は、一般的には、演算処理装置20によってこれらの阻害信号が減算され、重力の場Gに関する偏差計の測定精度を高めるようになっている。それについては、以下に図3を参照して説明する。演算処理装置20は、ハウジング16の内部に配置するように示してあるが、ハウジングの外部に配置するようにしてもよく、この演算処理装置によって偏差計からの測定値をリアルタイムに、または偏差計が重力の場Gを測定した後に演算する。後者の場合には、偏差計は通常はメモリ22を備えていて測定値を記憶し、後にそれを外部の演算処理装置20にダウンロードする。また、他の方法として、偏差計10に発信器（図示せず）を備え、測定値を外部の演算処理装置20および／または外部メモリ22に発信するようにしてもよい。さらに、演算処理装置20またはメモリ22にはサンプルおよびホールド回路（図示せず）とアナログ−デジタル変換装置（ADC）（図示せず）を備え、偏差計の測定値および最適な操作のためのその他の信号測定値をデジタル化する。 As shown in FIG. 1, a gravimeter 10 can be used to measure the field G of the geological potential (not shown). In the present invention, the nine tensor elements of the gravity field are represented by the following determinant:
(1)

Here, each matrix element represents a gravity tensor in the directions of the axes “X”, “Y”, and “Z” of three “body” intersecting at the body center 12 of the gravity deviation meter 10. For example, the tensor element Γxx is the gravitational acceleration vector g
Is the spatial partial derivative of the X component of the X component with respect to the X axis (where the tensor element is expressed in equivalent units (meters / second ² ) / meter or 1 / second ² , or in Etoves units, 109 etevs = 1 / second ² Is). Γxy is the spatial partial derivative of the X component of g with respect to the Y axis, Γxz is the spatial partial derivative of the X component of g with respect to the Z axis, and Γyx is the spatial partial derivative of the Y component of g with respect to the X axis. It is. Further, although the tensor element Γ can change with time, in many geological cases, the tensor element Γ is constant with respect to time, or may be treated as constant with respect to time. It changes slowly. Further, in some cases, the gravitational deviation meter 10 may perform measurement such that it is sufficient to calculate only the required elements of the total tensor Γ. Next, in order to measure the gravity potential field G of the geology (not shown in Fig. 1), the gravity deviation meter 10 is mounted on a vehicle (not shown) such as a helicopter and the gravity deviation meter is measured from above the topography. May scan. Thus, when scanning the geology from above, in order to obtain the highest accuracy, it is desirable that the gravimeter 10 does not rotate at high speed about the body axes X, Y, and z . Unfortunately, however, the vehicle often generates vibrations (e.g., by the engine) or is subjected to vibrations (e.g., by wind), causing the body shaft to undergo rotation. Therefore, the gravity deviation meter 10 is often non-rotated even when the vehicle is turned off by a gimbal device (not shown) and even if the vehicle undergoes an unavoidable change of direction when operating. Is supposed to maintain. The gimbal device carrying the gravitational deviation meter 10 generally includes a rotation sensor assembly 18 such as a gyroscope assembly, and rotates around the body axes X, Y, and Z (generally Rotational speed ω or rotational displacement) is measured. Control signals obtained from these measured values are fed back to the motor associated with the gimbal device shaft to reduce the rotation received by the gravity deviation meter 10. However, although the degree of rotation of the gravity deviation meter 10 induced by vibration is generally reduced by the gimbal device, it is impossible to eliminate all of these rotations. Therefore, even if an ideal deviation meter is used for the tensor measurement, it cannot be physically avoided that the tensor measurement may be hindered by the presence of the gradient signal due to the rotation as described above. These additional gravitational gradients (deviations) are functions that can be easily determined from the rotational speed (for example, when the rotational speed around the body axis j is ωj radians / second, Γ = ωx, ωy due to rotation). Therefore, the measured value from the deviation meter 10 is generally such that these inhibition signals are subtracted by the arithmetic processing unit 20 to increase the measurement accuracy of the deviation meter with respect to the gravity field G. This will be described below with reference to FIG. Although the arithmetic processing unit 20 is shown to be arranged inside the housing 16, it may be arranged outside the housing, and the arithmetic processing unit can measure the measured value from the deviation meter in real time or the deviation meter. Calculates after measuring the gravity field G. In the latter case, the deviation meter usually has a memory 22 to store the measured value and later download it to the external processing unit 20. As another method, the deviation meter 10 may be provided with a transmitter (not shown), and the measured value may be transmitted to the external arithmetic processing unit 20 and / or the external memory 22. Further, the processing unit 20 or the memory 22 is provided with a sample and hold circuit (not shown) and an analog-digital converter (ADC) (not shown), and the measured value of the deviation meter and others for optimal operation Digitize the measured signal value.

  Next, FIG. 2 will be described. The gravity deviation meter 10 shown in FIG. 1 comprises one or more disk assemblies, in this case three disk assemblies 24, 26, 28, each of which is a full set of tensors for the gravity field G of the geology 36. Measure a subset of Γ.

  Each disk assembly 24, 26, and 28 includes a disk 30, 32, and 34, respectively. These discs 30, 32, and 34 are mounted on the same or parallel to one of the three surfaces formed by the three main body shafts. As a result, the spin axes of these disks are the same as or parallel to the body axis perpendicular to the mounting surface. In addition, each disk has orthogonal disk axes that are within the mounting surface and simultaneously rotate relative to the surface. An example will be described below. The disk 30 is on the body axis plane XY, and has a spin axis ZS and orthogonal disk axes XD and YD. The spin axis ZS is parallel to the body axis Z, the X-Y coordinates of Zs are (X = C1, Y = C2), and C1 and C2 are constants. When the disk 30 is rotated—here counterclockwise—the disk axes XD and YD rotate relative to the non-rotating body axes X and Y. At the instant time shown in FIG. 2, the disk axes XD and YD of the disk 30 coincide with the body axes X and Y, respectively. Further, the disk 32 is on a plane parallel to the main body axis Y-Z and has a spin axis XS parallel to the main body axis X. At the instant time shown in FIG. 2, the disk axes XD and YD of the disk 32 are parallel to the body axes Y and Z, respectively.

In order to measure the gravitational field G, the disk assemblies 24, 26, and 28 each comprise at least a pair of accelerometers. Accelerometers are placed on each disk 30, 32, and 34 with a spacing of π radians. For clarity of explanation, only the disk assembly 24 will be described below, but the same applies to the other disk assemblies 26 and 28. Now, the disk assembly 28 includes two pairs of accelerometers 38a and 38b and 38c and 38d. Each accelerometer 38a, 38b, 38c, and 38d are respectively input shaft 40a, provided 40b, 40c, and 40d, which are intended for the respective acceleration _{A a, A b, A c} , and the Ad measuring . Each accelerometer is mounted on the disk 30 so that the input shaft is at a distance of radius R from the spin axis ZS and is orthogonal to R. Further, the first pair of accelerometers 38a and 38b are arranged at an interval of π radians on the disk axis XD, and the accelerometers 38c and 38d are arranged at an interval of π radians on the disk axis YD. In the above description, the ideal state is described as being orthogonal to the radius R. However, the input shafts 40a, 40b, 40c, and 40d may have other angles with respect to R depending on purpose or manufacturing convenience. May be. Further, another pair of accelerometers may be added to the disk assembly 24 and mounted between the accelerometers 38a, 38b, 38c, and 38d of the disk 30. For example, the disk assembly 24 may be provided with additional accelerometers 38e, 38f, 38g, and 38h that are spaced at π / 4 from the accelerometers 38a, 38b, 38c, and 38d, respectively. As is well known, increasing the accelerometer results in duplicate measurements when measuring the gravitational field, and has the effect of improving the signal-to-noise ratio (SN ratio).

  The operation of the disk assembly 24 will be described with reference to FIG. 3, but the operation of the disk assemblies 26 and 28 shown in FIG. 2 is the same.

  FIG. 3 is a plan view of the disk assembly 24. Here, the spin axis ZS extends from the center 50 of the disk 30 perpendicular to the paper surface. For the sake of explanation, the following ideal state is assumed. First, the disk 30 rotates counterclockwise at a constant speed Ω shown in units of radians / second. Secondly, the input shaft 40 is perfectly aligned with either the disk axis XD or YD, respectively, so that the input shaft is in or parallel to the XY plane. Third, all accelerometers are at the same radial distance R from the spin axis ZS. And fourth, the disk 30 does not rotate about the body axis X or Y.

式（2）を展開すると、
（３）

三角関数でcos²ΩtとcosΩtsinΩtは同等であること、および任意の重力の場において Γxy＝Γyxであることを利用して、以下の式が得られる。 At time t = 0, the disk axes XD and YD of the disk 30 coincide with the body axes X and Y, respectively. When the disk 30 rotates, the disk axis XD makes an angle Ωt with respect to the body axis X. Illustrating this rotation, the accelerometer 38a and the axes XD and YD are in broken line positions at Ωt = π / 4 radians. Although not shown by broken lines, the other accelerometers 38b, 38c, and 38d are also located at a position of π / 4 radians from the illustrated position (Ωt = 0) when Ωt = π / 4 radians. As a result, the acceleration A _a gravity tensor element Γxx, Γxy, Γyx, and be derived as the following equation, expressed in Ganmayy. Where ax and ay are accelerations due to gravity fields in the x and Y directions at the center 50, respectively. Specifically, A _a is equal to the value obtained by subtracting the acceleration component in the input axis direction due to the acceleration in the X direction from the acceleration component in the input axis 40a direction due to the acceleration in the Y direction.
That is,
(2)

Expanding equation (2)
(3)

Using the trigonometric function that cos ² Ωt and cosΩtsinΩt are equivalent, and Γxy = Γyx in an arbitrary gravity field, the following equation is obtained.

そして、式（4）をまとめると、
（５）

また、加速度計38bは加速度計38aに対して常にπラジアンの間隔を有しているから、加速度Abに対しては式（2）〜（5）の「Ωt」を「Ωt＋π」に置き換えることによって、下記の式を容易に導くことができる。 (4)

And when formula (4) is put together,
(5)

Also, since the accelerometer 38b always has an interval of π radians with respect to the accelerometer 38a, by replacing “Ωt” in equations (2) to (5) with “Ωt + π” for the acceleration Ab. The following formula can be easily derived.

式（5）と（6）を加算すると、これら二の加速度計の和の予想理想出力を以下の式によって与えることができる。 (6)

By adding equations (5) and (6), the expected ideal output of the sum of these two accelerometers can be given by

測定精度を向上させるために（以下に説明する起こり得る誤差の観点から）、式（2）〜（6）における「Ωt」をそれぞれ「Ωt＋π/2」および「Ωt＋3π/2」で置き換えることによって、AcとAdを重力テンソル要素Γxx、Γxy＝Γyx、およびΓyyで表す式を次のように導くことができる。 (7)

To improve measurement accuracy (in terms of possible errors described below), replace “Ωt” in Equations (2) to (6) with “Ωt + π / 2” and “Ωt + 3π / 2”, respectively, Expressions expressing Ac and Ad with gravity tensor elements Γxx, Γxy = Γyx, and Γyy can be derived as follows.

上記の二の加速度計の和（式7と8に示した）の差分を取ることによって次の式が得られる。この式がこの方法による偏差計測定の基礎的な要素となる。 (8)

By taking the difference of the sum of the two accelerometers (shown in equations 7 and 8), the following equation is obtained: This formula is the basic element of deviation meter measurement by this method.

この組合わせ信号は、通常は帯域信号と呼ばれるが、一般的に帯域フィルタをかけてデジタル化し、その後演算処理装置20によってsin2Ωtとcos2Ωtにおいて同期復調し、Γ_xy＝Γ_yxと（Γ_yy＝Γ_xx）/2を再生する。 (9)

This combined signal is usually called a band signal, but is generally digitized by applying a band filter, and then synchronously demodulated at sin2Ωt and cos2Ωt by the arithmetic processing unit 20, and Γ _xy = Γ _yx and (Γ _yy = Γ _xx ) / 2 is played.

  Still referring to FIG. Unfortunately, the conditions that have been assumed to be ideal for deriving equations (2) to (9) are often not ideal. Therefore, such a non-ideal condition introduces another acceleration term in the above formula, and if this other acceleration term is not properly processed, the accuracy of the calculated gravity tensor element is reduced. There is. However, advantageously, the processing unit 20 can process many of these other terms. This will be described below.

  Still referring to FIG. For example, a motor (not shown) that rotates the disk 30 may not be able to maintain a constant rotational speed Ω. When the rotational speed becomes non-uniform in this way, the pair of accelerometers detects the increased acceleration and crosses with the acceleration based on the gravity field. Therefore, the deviation meter 10 (FIG. 1) may include a sensor (not shown) that measures the rotational speed Ω. Then, the arithmetic processing unit 20 can include this measurement value in the acceleration term introduced into the equations (2) to (9) by non-uniform rotation.

  Further, as described above with reference to FIG. 1, vibrations and other forces of the vehicle (not shown) may cause the deviation meter 10 to rotate about the body axis X or Y. Such rotation also causes the pair of accelerometers to detect the increased acceleration, and crosses the acceleration due to the gravitational field. For example, it is assumed that the deviation meter 10 rotates about the main body axis Y at a rotational speed (unit: radians / second) ωy. By this rotation, the accelerometer 38a detects the centripetal acceleration directed in the Y-axis direction along the moment arm 52. This centripetal acceleration is given by the following equation, where AaY is an acceleration term added to equation (2) by centripetal acceleration.

加速度計38bも同等の求心加速度AbYを検出する。また、加速度計38cと38dもこれに相当する求心加速度AcYとAdYを検出するが、これらも式（10）の同様の式によって与えられる。このようにして、演算処理装置20は回転速度ωx、ωy、およびωzをあらわす信号（図1のジャイロスコープ18から得られる）を式（9）のAaY、AbY、AcY、およびAdYに算入することによって、勾配測定値から、本体軸X、Y、およびZを中心とする回転によって導入された求心力による誤差を補正することができる。 (10)

The accelerometer 38b also detects the equivalent centripetal acceleration AbY. The accelerometers 38c and 38d also detect the corresponding centripetal accelerations AcY and AdY, which are also given by a similar equation of equation (10). In this way, the arithmetic processing unit 20 adds the signals (obtained from the gyroscope 18 in FIG. 1) representing the rotational speeds ωx, ωy, and ωz to AaY, AbY, AcY, and AdY in Equation (9). Thus, the error due to the centripetal force introduced by the rotation about the body axes X, Y, and Z can be corrected from the gradient measurement value.

  Similarly, based on the fact that the paired accelerometer input shafts 40 do not form the same angle as the disk axis XD or YD, respectively, or do not form the same radial distance R from the disk center 50. Errors can also be processed by the arithmetic processing unit 20 in many cases. In such cases, the exact magnitude of misalignment and radial distance error is generally unknown (relatively constant or incomplete but known for a given deviation meter). Although there is, it is impossible to know exactly the error introduced in the measurement of the gravitational field. However, if the functional relationship between the causative error and the resulting signal blockage is known, when this is introduced into the calculation procedure, the test measurement is processed and determined to be blocked Optimum fitting is performed between the measured values, and finally, correction can be performed using these optimum fitting calculation results. In most cases, there is a linear (or linearizable) relationship between the error parameter and the resulting signal inhibition, and an arbitrarily scaled calculation of the inhibited measurement and expected signal inhibition. A standard least squares fit can be made between the values. These prediction functions are called regression values, and the fit calculation procedure can calculate the degree of fit between these regression values and the original measured values.

  Unfortunately, however, there is no combination of regression values that fits all the acceleration and rotation errors that can be obtained with a deviation meter system. Therefore, to improve the performance of the deviation meter, it is important to identify the source of the error, estimate and correct the error effect obtained with a specific device, and if possible, create the device And adjustments during installation reduce physical effects that can lead to errors.

  The embodiment of the present invention described below finds one of the error mechanisms as described above, and calculates the error effect due to this mechanism (thus, it is possible to improve the correction and measurement performance). In order to reduce the magnitude of the effect of errors, the present invention relates to determining a device adjustment method.

  One aspect of the present invention is a method that includes measuring acceleration and calculating a gravity tensor element. As for the acceleration measurement, the acceleration along the input axis of the accelerometer mounted on the deviation meter disk is measured. This accelerometer has a coordinate axis parallel to the spin axis of the disk. Further, the gravity tensor element is calculated as a function of the acceleration measurement value and the component of the acceleration measurement value resulting from the acceleration along the coordinate axis.

  This technique can perform more accurate calculation of the gravitational field by processing unnecessary acceleration detected by an accelerometer having an input axis that is not parallel to the deviation meter disk. This approach can also be applied to systems that measure a full set of gravity tensors and to systems that measure a subset of the full set of tensors.

  The following description is made to enable one of ordinary skill in the art to make and use the invention. It will be apparent to those skilled in the art that various modifications can be made to this embodiment, and the generic principles described herein can be applied to other embodiments, Applications that do not depart from the spirit and scope of the invention are defined by the appended claims. Accordingly, the present invention is not limited to the illustrated embodiments and is to be applied to the maximum extent consistent with the principles and features disclosed herein.

  4A and 4B are side views of first and second accelerometers 60a and 60b, respectively, of a pair of accelerometers according to an embodiment of the present invention. Referring to FIG. 3, accelerometers 60a and 60b are mounted on the same as disk 30, and are arranged at an interval of π radians similarly to accelerometers 38a and 38b. However, while the accelerometers 38a and 38b are ideally oriented, the input shafts 62a and 62b of the accelerometers 60a and 60b are often parallel to the disk due to manufacturing variations. It is not. Therefore, an extra acceleration term is introduced into the equations (2) to (9). Each accelerometer 60a and 60b has a coordinate system with 64a and 64b as origins, respectively. Describing the accelerometer 60a, the ZA axis is parallel to the disk spin axis ZS. The YA axis is parallel to the disk and is orthogonal to the radius of the disk at the origin 64a. Furthermore, the XA axis coincides with the radius of the disk passing through the origin 64a. That is, the XA axis passes through the origin 64a and is perpendicular to the paper surface. Similarly, the accelerometer 60b will be described. The ZB axis is parallel to the spin axis ZS of the disk. The YB axis is parallel to the disk and is orthogonal to the radius of the disk at the origin 64b. Further, the XB axis coincides with the radius of the disk passing through the origin 64b, and is perpendicular to the paper surface through the origin 64b.

  FIG. 4A will be described. The accelerometer 60a measures the acceleration component that appears along the ZA axis and adds it to the acceleration terms of the equations (2) to (9). Therefore, if these accelerations are not deleted from the acceleration measurement value, an error is introduced into the calculation of the gravity tensor element. Specifically, the input shaft 62a of the accelerometer 60a forms a non-zero angle βa with respect to the YA axis. This is different from the input shaft 40a of the accelerometer 38a (FIG. 3) being at a zero angle (βa = 0) with respect to the YA axis (not shown in FIG. 3). Therefore, since the input shaft 62a has a projection length with respect to the ZA axis, the accelerometer 62a measures the acceleration term AaZ with respect to Aa in response to the acceleration AZA in the ZA axis direction. This AaZ is given by the following equation.

従って、重力の場の計算の際に、軸方向の位置ずれ、すなわちβa、の効果を正確に反映するためには、AaZの項を式（2）〜（5）の右辺に含めなければならない。同様にして図4Bを参照する。加速度計60bは加速度AZB（すなわち、64b点におけるZB方向の加速度）に応答して、Abの加速度項AbZを測定する。AbZは次式で与えられる。 (11)

Therefore, the term AaZ must be included in the right side of Equations (2) to (5) to accurately reflect the effect of axial displacement, ie, βa, when calculating the gravitational field. . Similarly, refer to FIG. 4B. The accelerometer 60b measures the acceleration term AbZ of Ab in response to the acceleration AZB (that is, the acceleration in the ZB direction at the point 64b). AbZ is given by the following equation.

そして、βbの効果を正確に反映させるためには、AbZの項を式（6）の右辺に含めなければならない。 (12)

In order to accurately reflect the effect of βb, the term AbZ must be included on the right side of Equation (6).

  Referring to FIGS. 1, 4A, and 4B, and assuming that accelerometers 60a and 60b are installed instead of accelerometers 38a and 38b, one cause of accelerations AZA and AZB in the ZA and ZB axis directions is That is, non-rotational acceleration in the spin axis ZS direction. As an example, a vehicle equipped with the deviation meter 10 may be accelerated in the Z-axis direction by a gust of wind. In this case, AZA = AZB = AZS.

As an existing method for eliminating the acceleration terms Aaz and Abz introduced in equations (2) to (9) by such non-rotational acceleration, accelerometers 60a and 60b are placed on disk 30 and βb = − It may be worn so as to have a βa relationship. The accelerations Aa and Ab are added according to the equation (7) to obtain the following equation. Aaz + Abz = AZ _s sinb _a + AZ _s sinb _b = AZ _s sinb _a −AZ _s sinb _b = 0. Further, even if the accelerometers 60a and 60b cannot be accurately mounted so that βb = −βa, βb can be set close to −βa in many cases. In that case, Aaz + Abz Can be ignored and Aaz and Aab can be eliminated from equations (2)-(9). However, in general, Aaz + Abz cannot be ignored, and the displacements βa and βb are too small to be recognized using the conventional accelerometer correction method. Therefore, as one method developed for the deviation meter, a common (ie non-rotating) acceleration is introduced in the Zs axis direction, and the signal is added during the process of inspecting the accelerometer, so that the common part of the displacement is There is a way to recognize. This acceleration can be introduced by a correction device in a correction process before shipping the deviation meter. As another method, there is a method in which the deviation meter performs self-correction using acceleration generated by a vehicle equipped with an accelerometer. In this method, the net effect of all accelerometers is made zero by adjusting the axial displacement of one arbitrarily selected accelerometer. That is, sinβa + sinβb + sinβc + sinβd = 0. Where βc and βd are acceleration terms from the other pair of accelerometers, which are similar to accelerometers 60a and 60b, respectively, and ideal accelerometers 38c and 38d (FIG. 3). ) Is mounted on the disc 30 as an alternative. If the ability to correct this net misalignment is better than the ability to realign the accelerometer (ie sinβa + sinβb + sinβc + sinβd ≠ 0), the measurement of the processing unit 20 (Figure 1) Change the value processing algorithm to include correction for the net effect of Aaz, Abz, Acz, and Adz (where Acz and Adz are accelerations from another pair of accelerometers) in Equation (9) Thereby improving the measurement results. These existing methods are effective in eliminating the common axial (Zs) acceleration, but cannot recognize or reduce the effect of individual axial misalignment. Accordingly, as described below, one embodiment of the present invention addresses such deficiencies.

  Description will be made with reference to FIGS. 1, 4A, 4B, and 5 again. Assuming that disk 30 is equipped with accelerometers 60a and 60b instead of accelerometers 38a, 38b, 38c, and 38d, and another pair of accelerometers corresponding to them, acceleration AZA is generated in the ZA axis direction. Another factor is rotational acceleration (α = dω / dt, where ω is the rotational speed described above) about the axis X or Y of the deviation meter 10. Unfortunately, the acceleration introduced by these rotational accelerations cannot be reduced or eliminated by setting βb = −βa, as explained below.

  FIG. 5 is an end view of the disk 30 taken along the line AA in FIG. Here, the accelerometers 38a and 38b are replaced by the accelerometers 60a and 60b shown in FIGS. 4A and 4B. The accelerometers 38c and 38d are replaced by the same accelerometers as the accelerometers 60a and 60b, and their input axes are at angles βc and βd with respect to the ZC and ZD axes, respectively. The acceleration term introduced by the rotational acceleration α is included in the equations (2) to (9) according to the embodiment of the present invention.

  The normal position of the disk 30 is indicated by a solid line. In the normal position where Ωt = 0, the disc axes XD and YD (perpendicular to the paper surface) coincide with the main body axes X and Y (perpendicular to the paper surface), respectively, and the spin axis ZS is parallel to the main body axis Z. is there.

  When rotational acceleration, for example, acceleration αy occurs in the counterclockwise direction around the body axis Y, the disk 30 is accelerated in the direction of the position indicated by the broken line. When βa and βb have opposite signs, the acceleration component Aaz (αy) measured by the accelerometer 60a is increased by the acceleration component Abz (αy) measured by the accelerometer 60b. For a more specific description, refer to FIG. 4A. Since the input shaft 62a of the accelerometer 60a has a projection length on the positive axis ZA, the accelerometer 60a measures the positive acceleration Aaz (αy) corresponding to the rotational acceleration αy. Similarly, refer to FIG. 4B. Since the input shaft 62b of the accelerometer 60b has a projection length on the negative axis ZB, the accelerometer 60b measures the positive acceleration Abz (αy) due to the rotational acceleration αy. As a result, unlike the terms Aaz and Abz (equations (11) and (12)) introduced by non-rotational acceleration described above in connection with FIGS. 4A and 4B, they are introduced by rotational acceleration αy. The term Aaz (αy) is augmented by Abz (αy) introduced by αy and is not eliminated. This is true even when βa = −βb.

  Referring to FIGS. 3, 4A and 5, the acceleration term Aaz (αy) introduced by αy is a function of the length of the moment arm 52 and the projected length of the input shaft 62a on the ZA axis, and is therefore given by .

そして、本体軸Xを中心とする回転加速度αxによって導入される加速度項Aaz(αx)は次式で与えられる。 (13)

The acceleration term Aaz (αx) introduced by the rotational acceleration αx about the body axis X is given by the following equation.

そして、他方の加速度計60bおよび、他の一対の加速度計によるによる誤差加速度項は、次式で与えられる。 (14)

The error acceleration term due to the other accelerometer 60b and the other pair of accelerometers is given by the following equation.

X−ZまたはY−Z面内にあるか、またはこれらに平行なディスクについても同様の解析が可能である。

Similar analysis is possible for discs that are in or parallel to the XZ or YZ plane.

  By including in the equation (9) the above acceleration term and the measured value from the rotation sensor assembly 18 (FIG. 1), the arithmetic processing unit 20 can detect the axial displacements βa, βb, βc, and These measurement errors can be processed based on βd. When the terms of the equations (14) to (20) are included in the equation (9) and the result in the ideal state (the right side of the equation (9)) is reduced, the following equation is obtained with respect to the error induced by the rotational acceleration.

上述した非回転型の加速度に関する誤差補正と同様にして、この情報は勾配測定の改良に関して様々な手法に利用することができる。位置ずれβa、βb、βc、およびβdの補正が終了すると、演算処理装置20によって位置ずれの結果発生していた誤差は簡単に計算され、削除することができる。逆に、補正手順の過程で得られた誤差を含む勾配と、回転センサ組立体18（図1）によって得られた測定値間で最適適合を行うことによって、これらの位置ずれの補正を実行することも可能である。既述したように、回転補正した加速度は、補正／試験機器を利用して、偏差計の出荷前補正の過程で導入することができる。また、他の方法として、偏差計が搭載される乗物が発生する回転加速度を利用して偏差計が自己補正するようにすることも可能である。 (21)
Signal error introduced by rotational acceleration =

Similar to the error correction for non-rotational acceleration described above, this information can be used in a variety of ways for improving gradient measurements. When the correction of the positional deviations βa, βb, βc, and βd is completed, the error that has occurred as a result of the positional deviation is easily calculated by the arithmetic processing unit 20 and can be deleted. Conversely, these misalignments are corrected by making an optimal fit between the gradient, including the error obtained during the correction procedure, and the measured value obtained by the rotation sensor assembly 18 (FIG. 1). It is also possible. As described above, the rotation-corrected acceleration can be introduced in the process of the deviation meter before shipping using the correction / test equipment. As another method, the deviation meter can self-correct using the rotational acceleration generated by the vehicle on which the deviation meter is mounted.

  Furthermore, this technique can be applied to a disk in the XY or YZ plane as well. It is also possible to predict other embodiments of the present invention. For example, the rotation sensor assembly 18 (FIG. 1) may be partially or completely disposed on the rotating disk 30. In this case, it is not necessary to decompose the detected rotation into the accelerometer frame included in sin (Ωt) and cos (Ωt) in equation (21). Furthermore, since the disk is in a plane that does not coincide with or is not parallel to any of the body axes X-Y, X-Z, or Y-Z, equations (11)-(21) are well known mathematical principles Can be modified according to. Further, when the disk 30 is at the position of Ωt = 0, the angles βa and βb can be determined by a conventional method such as rotating the disk around the axis YD at a known rotational acceleration.

FIG. 1 is a diagram showing a conventional gravity deviation meter. FIG. 2 is a view showing a conventional deviation meter disk assembly inside the gravity deviation meter shown in FIG. FIG. 3 is a plan view of one deviation meter of the disk assembly shown in FIG. 4A and 4B are side views of the first and second accelerometers, respectively, of a pair of accelerometers according to embodiments of the present invention. FIG. 5 is a side view of a deviation meter disk assembly that rotates about a non-spin axis according to an embodiment of the present invention.

Claims (20)

A gravity deviation meter, which has a spin axis , a disk having a radial axis perpendicular to the spin axis, and a coordinate axis and an input axis that are mounted on the disk along the disk axis and are parallel to the spin axis of the disk. And an accelerometer capable of measuring the acceleration input in the direction of the input axis, and a gravitational tensor element can be calculated as a function of the acceleration term by the acceleration in the direction of the coordinate axis of the accelerometer. The gravity deviation meter comprising: an arithmetic processing unit. The gravity deviation meter according to claim 1, further comprising a rotation sensor assembly connected to the arithmetic processing unit and capable of measuring an angular acceleration of a disk about an axis parallel to the disk. in those de, this acceleration is characterized in that it is a function of the angular acceleration measurement value, the gravity gradiometer. In the gravity gradiometer according to claim 1, wherein the input shaft of said accelerometer and wherein the coordinate axis of the accelerometer and are separated at an angle, and the acceleration is a function of angle, the Gravity deviation meter. 2. The gravity deviation meter according to claim 1, wherein the arithmetic processing unit is capable of processing the acceleration term on the assumption that the disk is fixed. A gravity deviation meter, a housing having first, second, and third orthogonal body axes, a first mounted on the inside of the housing, orthogonal to the spin axis and the spin axis. A disc having a first radial disc axis, an accelerometer mounted on the disc, having a coordinate axis parallel to the spin axis of the disc and an input axis, and capable of measuring input acceleration in the input axis direction; A rotation sensor assembly mounted inside the housing and capable of measuring the rotation of the housing about the first, second and third body axes, and an arithmetic processing unit connected to the sensor assembly. In this configuration, the arithmetic processing unit calculates an input acceleration measurement value and a component of the input acceleration measurement value resulting from rotation of the housing around the first, second, and third body axes. By solving equations including a to the acceleration term, characterized in that it is possible to calculate the weight tensor elements, the gravity gradiometer. 6. The gravity deviation meter according to claim 5, wherein the input shaft of the accelerometer is separated from the disk by an angle, and the acceleration term is a function of the angle. . 7. The gravity deviation meter according to claim 6, wherein the second and third body axes are on a first surface, the disk is on a second surface substantially parallel to the first surface, and the acceleration term. Is a function of the angle between one of the first and second disk shafts and one of the second and third body shafts. A method of measuring an acceleration in an input axis direction of an accelerometer mounted on a disc of a deviation meter and having a coordinate axis parallel to a spin axis of the disc, the input acceleration measurement value, and the accelerometer Calculating a gravitational tensor element as a function of the first component of the acceleration measurement value resulting from the acceleration in the coordinate axis direction. 9. The method of claim 8, wherein the first component of the input acceleration measurement is a function of the rotational acceleration of the disk about an axis that is non-parallel to the spin axis of the disk. Method. 9. The method of claim 8, further comprising the step of measuring the rotational acceleration of the disk about an axis parallel to the disk, wherein the first component of the input acceleration measurement value is the rotational acceleration measurement value. The method of claim 1, wherein 9. The method of claim 8, wherein the step of calculating a gravitational tensor element comprises solving an equation that includes an input acceleration measurement and a known value of a component of the input acceleration measurement. Method. 9. The method according to claim 8, wherein the component of the input acceleration measurement value is a function of an angle between the coordinate axis of the accelerometer and the input axis. 9. The method of claim 8, wherein the step of calculating a gravity tensor element includes calculating the gravity tensor element as a function of a second component of an acceleration measurement resulting from acceleration in the direction of the coordinate axis of the accelerometer. And the first component of the input acceleration measurement is a function of the rotational acceleration of the disk about a first axis that is non-parallel to the spin axis of the disk, and the second component of the input acceleration measurement is The method of claim 1, wherein the method is a function of the rotational acceleration of the disk about a second axis that is non-parallel to the spin axis of the disk and orthogonal to the first axis. 9. The method of claim 8, wherein the step of calculating a gravity tensor element includes the step of calculating a gravity tensor element as a function of a second component of an acceleration measurement based on acceleration in the direction of the coordinate axis of the accelerometer. The first component of the input acceleration measurement value is a function of the rotational acceleration of the disk about a first axis orthogonal to the spin axis of the disk, and the second component of the input acceleration measurement value is the spin axis. And the method is a function of the rotational acceleration of the disk about a second axis orthogonal to the first axis. A method comprising: receiving an input acceleration measured along the radial axis of an accelerometer mounted along a radial axis of a rotating deviation meter disk; and a first body axis of a housing containing the disk And a step of calculating a gravitational tensor element from the input acceleration and a first component of the input acceleration, wherein the first component is the rotational acceleration, the input shaft and the disk. The method is characterized in that it is a function of the angle formed by the surface. 16. The method of claim 15, further comprising the step of downloading the received input acceleration and the rotational acceleration to a processing unit disposed outside a housing, wherein the gravity tensor element is calculated by the processing unit. Characterized by the above. 16. The method of claim 15, wherein the first component of input acceleration is also a function of the angle formed by the disc axis and the first body axis. 16. The method of claim 15, further comprising receiving rotational acceleration about a second body axis that is orthogonal to the first body axis of the housing, wherein the step of calculating a gravitational tensor comprises input acceleration. Calculating a gravitational tensor element as a function of the second component of the second component, wherein the second component is a function of the rotational acceleration about the second body axis and the angle between the input shaft and the surface of the disk. Said method, characterized in that it is. A method for receiving input acceleration measured in the direction of an input axis of an accelerometer (s) mounted along an orthogonal axis of a rotating deviation meter disk; and a first orthogonal and a housing of a housing housing the disk Receiving a first and a second rotational acceleration about a second body axis; and calculating a gravitational tensor element from the input acceleration and first and second components of the input acceleration. The first component is a function of the first rotational acceleration and the angle formed by the input shaft and the surface of the disk, and the second component is a function of the second rotational acceleration and the angle formed by the input shaft and the disk surface. , Said method. 21. The method of claim 19, wherein the disk is parallel to a plane including first and second body axes, and the step of calculating a gravity tensor element is an angle formed by one of the disk axes and one of the body axes. A method comprising calculating a gravity tensor element as a function of.

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